This is a program I did when I saw a shape drawn with polar coordinates (I was done with my math test so i decided to look in a calculus book...I got a 73 on the test ) . I tried doing it myself. It just rotates a vector and multiplies each by a sine wave.
One is the sine of the angle * 4, one is the sine of the angle * 3, and one is the sine of an exponential model that is increasing and decreasing at a certain percent in a sine fashion (goes up, goes down, goes up, goes down, etc). The color and blended transparencies also move in sine waves.
EDIT: and oh yeah, move around with w,a,s,d and mouse to see the other two things.